Résumé : Self-avoiding walks appear ubiquitously in the study of linear polymers as it naturally captures their volume exclusion property. However, self-avoiding walks are very difficult to analyse with few rigourous results available. In 2008, Alvarez et al. determined numerical results for the forces induced by a self-avoiding walk in an interactive slit. These results resembled the exact results for a directed model in the same setting by Brak et al. in 2005, suggesting the physical consistency of directed walks as polymer models. Via the kernel method, we extend the directed walk model to a series of models involving two directed walks as a way to find exact enumerative results for studying the behaviour of ring polymers near an interactive wall, or walls. In the final model we considered, we are unable to find exact solutions via the kernel method. Instead, we use transfer matrices to obtain numerical results that are qualitatively similar to those presented by Alvarez et al.
|Dernière modification : Thursday 17 December 2015||Contact : Cyril.Banderier at lipn.univ-paris13.fr|